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Related papers: Multi-interval Sturm-Liouville boundary-value prob…

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In this work we investigate the resolvent operator and completeness of eigenfunctions of a Sturm-Liouville problem with discontinuities at two points. The problem contains an eigenparameter in the one of boundary conditions. For…

Spectral Theory · Mathematics 2013-04-23 Erdoğan Şen , Oktay Mukhtarov , Kamil Oruçoğlu

In this paper we are concerned with a new class of BVP' s consisting of eigendependent boundary conditions and two supplementary transmission conditions at one interior point. By modifying some techniques of classical Sturm-Liouville theory…

Classical Analysis and ODEs · Mathematics 2013-03-28 O. Sh. Mukhtarov , K. Aydemir

The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…

Numerical Analysis · Mathematics 2016-04-15 Ricardo Almeida , Agnieszka B. Malinowska , M. Luísa Morgado , Tatiana Odzijewicz

We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals $(a,b) \subseteq \mathbb{R}$ associated with rather general differential expressions of the type \[ \tau f = \frac{1}{r} (-…

Spectral Theory · Mathematics 2013-04-30 Jonathan Eckhardt , Fritz Gesztesy , Roger Nichols , Gerald Teschl

We study the second order nonlinear differential equation \begin{equation*} u"+ \sum_{i=1}^{m} \alpha_{i} a_{i}(x)g_{i}(u) - \sum_{j=0}^{m+1} \beta_{j} b_{j}(x)k_{j}(u) = 0, \end{equation*} where $\alpha_{i},\beta_{j}>0$, $a_{i}(x),…

Classical Analysis and ODEs · Mathematics 2016-07-29 Guglielmo Feltrin

In this paper we are concerned with a new class of BVP' s consisting of eigendependent boundary conditions and two supplementary transmission conditions at one interior point. By modifying some techniques of classical Sturm-Liouville theory…

Classical Analysis and ODEs · Mathematics 2013-03-29 O. Sh. Mukhtarov , K. Aydemir

We continue the study of boundary data maps, that is, generalizations of spectral parameter dependent Dirichlet-to-Neumann maps for (three-coefficient) Sturm-Liouville operators on the finite interval $(a,b)$, to more general boundary…

Spectral Theory · Mathematics 2012-04-17 Stephen Clark , Fritz Gesztesy , Roger Nichols , Maxim Zinchenko

This paper deals with the computation of the eigenvalues of non self-adjoint Sturm-Liouville problems with parameter dependent boundary conditions using the \textit{regularized sampling method}. A few numerical examples among which singular…

Spectral Theory · Mathematics 2007-05-23 Bilal Chanane

Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville…

Numerical Analysis · Mathematics 2015-07-08 Philippe Gaudreau , Richard Slevinsky , Hassan Safouhi

In this work, we use the \textit{regularized sampling method} to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their…

Spectral Theory · Mathematics 2007-05-23 Bilal Chanane

Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2)…

Spectral Theory · Mathematics 2008-03-06 Namig J. Guliyev

In this paper, we find the minimizer of the eigenvalue gap for the single-well potential problem and the eigenvalue ratio for the single-barrier density problem and symmetric single-well (single-barrier)density problem for $p$-Laplacian.…

Classical Analysis and ODEs · Mathematics 2011-05-12 Y. H. Cheng , Wei-Cheng Lian , Wei-Chuan Wang

In this paper, we present a new approachment for Sturm-Liouville problem having special potentials. We acquire the representations of solutions and asymptotic formulas for solutions with regard to initial conditions. Also, a few…

Spectral Theory · Mathematics 2019-03-13 Erdal Bas , Ramazan Ozarslan

We consider the inverse Sturm-Liouville problem with one discontinuous point on three-star graph, we deduced the distribution of the eigenvalues, and proved that one spectrum could uniquely determine the unknown potential and jump…

Spectral Theory · Mathematics 2020-12-30 Kang Lv

Regular Sturm-Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this note we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the…

Spectral Theory · Mathematics 2013-06-04 Jussi Behrndt , Shaozhu Chen , Friedrich Philipp , Jiangang Qi

The self-adjoint and $m$-sectorial extensions of coercive Sturm-Liouville operators are characterised, under minimal smoothness conditions on the coefficients of the differential expression.

Spectral Theory · Mathematics 2016-04-13 B. M. Brown , W. D. Evans

We consider a Sturm--Liouville boundary value problem in a boun\-ded domain $\cD$ of $\mathbb{R}^n$. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in $\cD$ and the boundary…

Analysis of PDEs · Mathematics 2022-02-22 A. Shlapunov , N. Tarkhanov

One important innovation here is that for the Sturm-Liouville considered equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at one interior point. We develop Green's function…

Classical Analysis and ODEs · Mathematics 2013-03-29 K. Aydemir , O. Sh. Mukhtarov

In this paper, we investigate the sampling analysis for a new Sturm-Liouville problem with symmetrically located discontinuities which are defined to depending on a neighborhood of a midpoint of the interval. Also the problem has…

Classical Analysis and ODEs · Mathematics 2014-12-01 Fatma Hira , Nihat Altinisik

In this paper we develop certain aspects of perturbation theory for self-adjoint operators subject to small variations of their domains. We use the abstract theory of boundary triplets to quantify such perturbations and give the second…

Spectral Theory · Mathematics 2021-10-15 Yuri Latushkin , Selim Sukhtaiev